Deep learning has been emerging as a highly effective method for data-driven prognostic and health management (PHM) studies in the past years. Many machinery condition monitoring tasks have been largely benefited from the development of deep neural network-based algorithms, such as fault diagnosis, remaining useful life prediction and so forth. While successful applications can be found in the current literature with respect to the conventional health monitoring cases with a single system component, limited attention has been paid on the complex machinery systems with multiple components. In this paper, a deep learning-based framework is proposed for the health anomaly detection problem on multi-component systems. The convolutional neural network and long short-term memory models are adopted and improved for the specific PHM scenario. The relationship between different components is implicitly captured and leveraged by the deep neural networks for identifying the health conditions. Experiments on the multi-component condition monitoring dataset validate the effectiveness of the proposed method. The proposed framework can be also easily extended for additional deep learning models, and that is well suited for the multicomponent system PHM tasks.